Theorems · Theorem · real analysis
Real.rpow_logb
∀ {b x : ℝ}, 0 < b → b ≠ 1 → 0 < x → b ^ Real.logb b x = x- Cited by
- 15 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- LT.lt.ne'proof · cited by 1,417
- Real.logbstatement · cited by 119
- abs_of_posproof · cited by 114
- Real.rpow_logb_eq_absproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- Real.floor_logb_natCastproof · cited by 2
- Real.logb_le_iff_le_rpow_of_base_lt_oneproof · cited by 1
- Rat.AbsoluteValue.eq_one_of_not_dvdproof · cited by 1
- Rat.AbsoluteValue.equiv_real_of_unboundedproof · cited by 1
- Real.logb_lt_iff_lt_rpowproof · cited by 1
- Rat.AbsoluteValue.exists_pos_eq_pow_negproof · cited by 1
- Real.ceil_logb_natCastproof · cited by 1
- Real.logb_le_iff_le_rpowproof · cited by 1
- Real.le_logb_iff_rpow_leproof · cited by 1
- Real.le_logb_iff_rpow_le_of_base_lt_oneproof · cited by 0
- Real.logb_lt_iff_lt_rpow_of_base_lt_oneproof · cited by 0